Global structure of steady-states to the full cross-diffusion limit in the Shigesada-Kawasaki-Teramoto model

Kuto, Kousuke

doi:10.1016/j.jde.2022.06.002

Cited by 5 publications

(1 citation statement)

References 25 publications

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“…In the same way, the population moves toward higher density of another population if the cross‐diffusion rate is negative and the species tends to lower density of another species if the cross‐diffusion rate is positive. Unfortunately, nearly all researches in biomathematics have a confusing hypothesis that

d&gt;0

for convenience of discussion or realistic principle in biology 17–23 . Therefore, their models cannot illustrate various phenomena in a precise way.…”

Section: Introductionmentioning

confidence: 99%

Nonconstant steady states and pattern formations of generalized 1D cross‐diffusion systems with prey‐taxis

2023

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Cross-diffusion effects and tactic interactions are the processes that preys move away from the highest density of predators preferentially, or vice versa. It is renowned that these effects have played significant roles in ecology and biology, which are also essential to the maintenance of diversity of species. To simulate the stability of systems and illustrate their spatial distributions, we consider positive nonconstant steady states of a generalized cross-diffusion model with prey-taxis and general functional responses in one dimension. By applying linear stability theory, we analyze the stability of the interior equilibrium and show that even in the case of negative cross-diffusion rate, which appeared in many models, the corresponding cross-diffusion model has opportunity to achieve its stability. Meanwhile, in addition to the cross-diffusion effect, tactic interactions can also destabilize the homogeneity of predator-prey systems if the tactic interaction coefficient is negative. Otherwise, taxis effects can stabilize the homogeneity.

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d&gt;0

for convenience of discussion or realistic principle in biology 17–23 . Therefore, their models cannot illustrate various phenomena in a precise way.…”

Section: Introductionmentioning

confidence: 99%